As the opening chapter of and introduction to the volume, this chapter serves three main purposes. First, it sets out the conceptual and intellectual background of the book as a whole and outlines the rationale for the core aim, which is to foreground local communities and their practices – locality and agency. Second, it outlines three broad topics that organize the case studies and thus provide an overall structure. Third, it briefly introduces the specific local contexts investigated in each chapter and clarifies how these engage with the overall theme and objective of the volume.

This chapter examines what the designs of coins may tell us about the communities that commissioned them. Religious designs featured predominantly, often the presiding deity of a city or a design which referred to it. Mythology and topography also played an important role, often rooting coinages in their localities, and there were references to events or contemporary personalities. Comparisons can be made in relation to artistic work in other fields, such as gems, with a special reference to those who were involved in their creation – the engravers of the dies from which the coins were struck. The engraving of coin dies appears to have been regarded as an artistic exercise, and the appearance of signatures on coins offers a window onto part of the chaîne opératoire of coin production.

This chapter uses aspects of numismatic evidence (circulation and weight standards) to examine what coinage can tell us about connectivity and regionalism in Archaic Greece. Coinage spread westwards and northwards from its beginnings in around 550, first in the Aegean basin (Aegina and other islands), mainland Greece (Athens, Corinth, Boeotia, Thessaly) and further north (Thrace and Macedonia). By 480 it had been adopted by a wide range of communities, but they represented only a minority of known states. They are characterised by a number of different weight standards – principally the Euboeic, Aeginetan, Corinthian and Attic. Early Athenian coinage consisted of the so-called Wappenmünzen, but these were succeeded in the late sixth century by the famous ‘owls’. However, Aegina was probably the first place in mainland Greece to have made coins, from about 550, and its plentiful coinage circulated widely. Corinthian coinage was also influential. Northern Greece saw several zones of production, while inland tribal communities produced very large coins as a way of exporting the silver from their mines. All these coins circulated together and are found in hoards all over the eastern Mediterranean, having been used in trade and mercenary payments. A link with trireme warfare is also explored.

The explosion of Greek (and Phoenician) settlements around the shores of the Mediterranean and the Black Sea saw many of them adopt their own coinages with a rich iconographic repertoire, often religious in nature or reflecting a local activity such as viticulture. This chapter explores the evidence coinage offers for relationships between colonies and mother-cities, in some cases showing ongoing connections, in others showing the development of new regionalisms. Their coinages appeared quite soon after 550: in the east (Cyrene) and the west (mainly southern Italy, Sicily, but also southern France and Spain), while coinage in some of the cities of the Black Sea appeared early in the fifth century. Sources of silver are explored. Some nearby indigenous communities also made coins, adopting and adapting designs and weight standards.

The author proposes that new attention be paid to spaces hitherto considered marginal, which should be studied for themselves and no longer in negative relation to more developed areas, which they would separate or link by playing the role of buffer zones or transition zones. The interest of the markers proposed, based on the case of the Roman Gauls, is to highlight the diversity of forms of marginality, as well as their relativity.

This chapter gives an overview of several classical topics in the study of graph theory, including perfect matchings, Hamilton cycles, Eulerian trails, proper vertex- and edge-colourings, and connectivity. We begin by proving Hall’s theorem on perfect matchings, Kőnig’s theorem on vertex-covers, and Dirac’s theorem on the minimum degree threshold for a graph to contain a Hamilton cycle. The middle third of the chapter focuses on proper colourings; in particular, we give elegant proofs of Brooks’ theorem on vertex-colourings and Vizing’s theorem on edge-colourings. To finish the chapter, we prove the famous Max-Flow Min-Cut theorem of Ford and Fulkerson, and the fundamental theorems of Menger and Mader on k-connectivity

Volume I offers a broad perspective on urban culture in the ancient European world. It begins with chronological overviews which paint in broad brushstrokes a picture that serves as a frame for the thematic chapters in the rest of the volume. Positioning ancient Europe within its wider context, it touches on Asia and Africa as regions that informed and were later influenced by urban development in Europe, with particular emphasis on the Mediterranean basin. Topics range from formal characteristics (including public space), water provision, waste disposal, urban maintenance, spaces for the dead, and border spaces; to ways of thinking about, visualising, and remembering cities in antiquity; to conflict within and between cities, economics, mobility and globalisation, intersectional urban experiences, slavery, political participation, and religion.

Volume I offers a broad perspective on urban culture in the ancient European world. It begins with chronological overviews which paint in broad brushstrokes a picture that serves as a frame for the thematic chapters in the rest of the volume. Positioning ancient Europe within its wider context, it touches on Asia and Africa as regions that informed and were later influenced by urban development in Europe, with particular emphasis on the Mediterranean basin. Topics range from formal characteristics (including public space), water provision, waste disposal, urban maintenance, spaces for the dead, and border spaces; to ways of thinking about, visualising, and remembering cities in antiquity; to conflict within and between cities, economics, mobility and globalisation, intersectional urban experiences, slavery, political participation, and religion.

The human brain can be divided by both structure and function. Brodmann maps provide a useful way of organising the complex cortical structure based on cytoarchitecture. The basic architecture of the prefrontal cortex shows nothing substantially different to other cortical regions we have a clearer understanding of. However, it remains clear that there must be something anatomically different in the prefrontal cortex for it to be able to carry out such complex functions. Despite vast differences in the functionality of brain regions, topographic connectivity is considered a hallmark feature of cortical structure. However, relatively recent research evidence shows there may be more complexity to the connectivity pattern in the prefrontal cortex when viewed on a fine scale.

Functional magnetic resonance imaging (fMRI) is a noninvasive technique widely used in research to identify and characterize the neural correlates of human cognitive and affective processes. Here we provide a brief introduction to the physical and physiological bases of fMRI, as well as a description of some of the main analysis approaches. These include traditional approaches, such as those based on univariate general linear models, as well as more recent ones, including multivariate methods and connectivity measures. We discuss how these different techniques can be used to answer different, complementary scientific questions, providing some examples to illustrate this. We end with a discussion of some of the key issues, both in terms of experimental design and data acquisition, analysis, and interpretation, that should be considered when planning an fMRI study and that can be of particular interest to those new to the technique.

This chapter provides a focused examination of spatio-temporal analysis using multilayer networks in which each layer represents the instantiation of a spatial network at a particular time of observation. The nodes in all layers may be the same with the only differences being of edges among layers (a multiplex network) or the nodes may change or move between layers and times. Multilayer characteristics such as versatility (multilayer centrality) and spectral properties are introduced. Several examples are described and reviewed as model studies for future ecological applications.

Sets of points can be analysed from their positions in space and line segments can be studied separately for their own spatial arrangements and relationships. Combining points and lines as the nodes and edges of a spatial graph provides a flexible and powerful approach to spatial analysis. Such graphs and their network versions are studied by Graph Theory, a branch of mathematics that quantifies their properties, with or without additional features such as labels, weights and functions associated with the nodes and edges. Some relevant graph theory terms are introduced, including connectivity, connectedness, modularity and centrality. Networks are graphs with additional features, usually representing an observed system of interest, whether aspatial like a food web or spatial like a metacommunity. Key concepts for the latter example are connectivity, migration and network flow.

Hillslopes may be regarded as conveyor belts transferring water and sediment and nutrients to other parts of the geomorphic system. This chapter examines the mechanisms of, and the factors controlling, how far and how fast water, sediment and nutrients move along this conveyor belt, discussing water movement in and on hillslopes, fluid-gravity and sediment-gravity movement of sediment and nutrient movement. Hillslope processes do not operate in isolation, and the interaction, of connectivity among processes is also important. This interaction is particularly significant when assessing the importance of connectivity to understanding hillslopes within the context of landscape evolution. A full description of the connectivity of hillslope processes will require combined knowledge of both the magnitude–connectivity relationship, the probability distribution of event magnitudes and, to explain specific cases of functional connectivity, the actual sequence of events. In recent years there has been a growing recognition of the importance of connectivity in understanding the effects of hillslope processes. At best, however, that understanding remains patchy and incomplete.

This chapter discusses what is meant by connectivity in fluvial systems and how the connectivity approach differs from preceding research, the way in which it increases understanding of fluvial processes, and how knowledge of mechanisms and dynamics of processes fits into this framework. The focus is on longitudinal connectivity through river systems, mainly in large catchments and river channels and much of the attention is on sediment connectivity. The application of connectivity indices and graph theory are exemplified and the patterns, distributions and controls produced by connectivity analysis are demonstrated. Lateral connectivity is important in relation to the link of channels to floodplains and in maintaining functioning of wetlands. Recent developments of techniques and models have allowed additional factors to be incorporated and controls on connectivity of fluvial processes to be identified. The use of connectivity analysis as a framework is highly beneficial in management of fluvial systems and facilitates targeting of hotspots of sediment accumulation or depletion.